Question

simplify the expression to a + bi form: -\sqrt{16}+\sqrt{-1}-\sqrt{9}+\sqrt{-16}
answer attempt 1 out of 2

Explanation:

Step1: Simplify square - roots of positive numbers

We know that $\sqrt{16}=4$ and $\sqrt{9} = 3$. So the real - part related terms are $-\sqrt{16}-\sqrt{9}=-4 - 3=-7$.

Step2: Simplify square - roots of negative numbers

Recall that $\sqrt{-1}=i$ and $\sqrt{-16}=\sqrt{16}\times\sqrt{-1}=4i$. So the imaginary - part related terms are $\sqrt{-1}+\sqrt{-16}=i + 4i=5i$.

Step3: Combine real and imaginary parts

Combining the real and imaginary parts, the expression $-\sqrt{16}+\sqrt{-1}-\sqrt{9}+\sqrt{-16}$ simplifies to $-7 + 5i$.

Answer:

$-7 + 5i$